Quantum Suppression of Mass Inflation in Reissner-Nordstr\"{o}m Interiors via Wheeler-DeWitt Equation

Abstract

We construct a canonical quantization, the Wheeler-DeWitt equation, of the interior geometry of static and spherically symmetric black holes in Einstein-Maxwell-$\Lambda$ framework, focusing on Reissner-Nordstr\"{o}m. The wave function of the Wheeler-DeWitt equation for the Reissner-Nordstr\"{o}m black hole is set to be on-shell and exhibiting exponential damping away from the classical locus. Horizon boundary conditions for the wave function generate two regimes: a single inward mode from event horizon yields monotonic decay, while superpositions produce either a quantum bounce (single time arrow) or interference-driven annihilation-to-nothing (two time arrows). We show that these are generic features of static black hole interiors. Furthermore, the wave function of the Schwarzschild black hole, obtained as the charge-neutral limit of the Reissner-Nordstr\"{o}m black hole, is monotonically decaying and no longer unbounded. Moreover, this framework unifies classical and quantum interiors, suggests a quantum gravitational suppression to the mass inflation, and motivates extensions to Kerr and regular black holes.